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For the philosopher, scientist, archaeologist, art historian, biologist, poet and artist, as well as the general reader who wants to understand more about the fascinating properties of numbers and geometry, and their relationship to art and life, this is a thought-provoking book.show more

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Is everything chaos and chance, or is there order, harmony, and proportion in human life, nature, and the finest art? Can one find a natural aesthetic that corresponds to a universal order? If so, what importance can it have for the scientist, artist, or layman? What is the "true" significance of the triangle, rectangle, spiral, and other geometric shapes? These are but a few of the questions that Professor Matila Ghyka deals with in this fascinating book. The author believes that there are such things as "The Mathematics of Life" and "The Mathematics of Art," and that the two coincide. Using simple mathematical formulas, most as basic as Pythagoras' theorem and requiring only a very limited knowledge of mathematics, Professor Ghyka shows the fascinating relationships between geometry, aesthetics, nature, and the human body.
Beginning with ideas from Plato, Pythagoras, Archimedes, Ockham, Kepler, and others, the author explores the outlines of an abstract science of space, which includes a theory of proportions, an examination of "the golden section," a study of regular and semi-regular polyhedral, and the interlinking of these various shapes and forms. He then traces the transmission of this spatial science through the Pythagorean tradition and neo-Pythagorism, Greek, and Gothic canons of proportion, the Kabbala, Masonic traditions and symbols, and modern applications in architecture, painting, and decorative art. When we judge a work of art, according to his formulation, we are making it conform to a pattern whose outline is laid down in simple geometrical figures; and it is the analysis of these figures both in art and nature that forms the core of Professor Ghyka's book. He also shows this geometry at work in living organisms. The ample illustrations and figures give concrete examples of the author's analysis: the Great Pyramid and tomb of Rameses IV, the Parthenon, Renaissance paintings and architecture, the work of Seurat, Le Corbusier, and flowers, shells, marine life, the human face, and much more.
For the philosopher, scientist, archaeologist, art historian, biologist, poet, and artist as well as the general reader who wants to understand more about the fascinating properties of numbers and geometry, and their relationship to art and life, this is a thought-provoking book.
Dover unabridged and slightly corrected republication of the 1946 edition.show more

Table of contents

CHAPTER I PROPORTION IN SPACE AND TIME
Ratio and proportion.
"The simplest asymmetrical division of a measurable whole into two parts, and Ockham's principle of economy."
Generalisation of the concept of proportion.
"Arithmetical, geometrical and harmonic proportion."
The ten types of proportion.
"Proportion, symmetry, eurhythmy."
Rhythm in space and proportion in time.
CHAPTER II THE GOLDEN SECTION
Algebraical and geometrical properties of the Golden Section or Number F.
The Fibonacci Series and the Golden Section.
The F Rectangle.
"Phyllotaxis and "Ideal Angle" in botany."
The Golden Section and pentagonal symmetry.
CHAPTER III GEOMETRICAL SHAPES ON THE PLANE
Polygons.
Regular polygons and star-polygons.
"Remarkable triangles: Triangle of Pythagoras, Triangle of Price, "Sublime" Triangle."
Rectangles: the F Rectangle and the vF Rectangle.
"Pentagon, pentagram, decagon, and Golden Section."
Hexagon and oxtagon.
CHAPTER IV GEOMETRICAL SHAPES IN SPACE
The five regular polyhedra or Platonic bodies.
The thirteen semiregular Archimedian bodies.
Regular prisms and anti-prisms.
The two continuous star-dodecahedra of Kepler.
"The dodecahedron, the icosahedron and the Golden Section."
Other remarkable volumes.
"The "Chamber of the King" in the Great Pyramid."
"The Great Pyramid, star-dodecahedron, and the human body."
Regular hypersolids in the fourth dimension.
CHAPTER V THE REGULAR PARTITIONS ON THE PLANE AND IN SPACE
"Equipartitions and partitions of the plane, regular and semi-regular."
Equipartitions and partitions of space.
Crystal lattices.
Hexagonal and cubic symmetries.
The cuboctahedron and the close-packing of spheres.
"The principle of least action, most general law for inorganic systems."
CHAPTER VI THE GEOMETRY OF LIFE
Harmonious growth and logarithmic spiral.
Pentagonal symmetry in living organisms.
"Pentagon, F Spiral and Golden Section."
Flowers and shells.
The human body and the F Progression.
CHAPTER VII THE TRANSMISSION OF GEOMETRICAL SYMBOLS AND PLANS
Life and Legend of Pythagoras.
Pythagorean number-mystic.
"The Pythagorean tradition, the pentagram, decad and tetrakytus."
Neo-Pythagorism and Kabbala.
From the antique builders' guilds to the masons' guilds of the Middle Ages.
Masons' marks and fundamental design.
Masonic traditions and symbols.
CHAPTER VIII GREEK AND GOTHIC CANONS OF PROPORTION
Rediscovery of the Greek and Gothic canons of architecture.
Proportions and dynamic symmetry.
The dynamic rectangles of Hambidge and the directing circles of Moessel.
"Greek vases, Greek temples, and the human body."
Gothic master plans.
CHAPTER IX SYMPHONIC COMPOSITION
Periodic rediscovery of the Golden Section.
Seurat's divisionism.
Revival of Pythagorean doctrine in science and art.
"Modern applications of dynamic symmetry in architecture, painting, and decorative art."
Symphonic composition.show more